SemiParBIVProbit (version 3.2-4)

summary.SemiParBIVProbit: SemiParBIVProbit summary

Description

It takes a fitted SemiParBIVProbit object produced by SemiParBIVProbit() and produces some summaries from it.

Usage

## S3 method for class 'SemiParBIVProbit':
summary(object,n.sim=1000,s.meth="svd",sig.lev=0.05,thrs1=0.5,thrs2=0.5,...)

Arguments

object

A fitted SemiParBIVProbit object as produced by SemiParBIVProbit().

n.sim

The number of simulated coefficient vectors from the posterior distribution of the estimated model parameters. This is used to calculate `confidence' intervals for $\rho$.

s.meth

Matrix decomposition used to determine the matrix root of the covariance matrix. See the documentation of mvtnorm for further details.

sig.lev

Significance level used for intervals obtained via posterior simulation.

thrs1,thrs2

Threshold to calculate the correct prediction ratios for the two binary responses. Default value is 0.5. It only works when selection=FALSE.

...

Other arguments.

Value

• tableP1
  It returns a table containing parametric estimates, their standard errors, z-values and p-values for equation 1.
• tableP2
  As above but for equation 2.
• tableNP1
  It returns a table of nonparametric summaries for each smooth component including estimated degrees of freedom, estimated rank, approximate Wald statistic for testing the null hypothesis that the smooth term is zero, and p-value for equation 1.
• tableNP2
  As above but for equation 2.
• n
  Sample size.
• rho
  Estimated correlation parameter between the two equations.
• formula1
  The original GAM formula used for equation1.
• formula2
  The original GAM formula used for equation2.
• l.sp1
  Number of smooth components in equation 1.
• l.sp2
  Number of smooth components in equation 2.
• t.edf
  Total degrees of freedom of the estimated bivariate probit model.
• CIrs
  It returns `confidence' intervals for $\rho$.
• sel
  This is used for internal calculations.
• n.sel
  Number of selected observations in the sample selection case.
• npRE
  This is used for internal calculations.
• masses
  If npRE=TRUE, then it returns the probabilities associated with the biavariate mass points.
• table.npRE
  If npRE=TRUE, then it returns a table representing the estimated random effect distribution.
• table.R
  Joint absolute frequency table of observed binary value combinations. This as well as all remaining quantities below are not provided when selection=TRUE.
• table.P
  Joint absolute frequency table of predicted binary value combinations.
• table.F
  It is given by table.P/table.R.
• MR
  Based on the comparison between table.P and table.R, it reports the matching rate as percentage.
• P1,P2
  Marginal probabilities for the two binary outcomes y1=1 and y2=1.
• QPS1,QPS2
  Quadratic probability scores for the two binary responses as suggested by Diebold and Rudebusch (1989). Values are on the interval [0,2], with 0 indicating a perfect fit.
• CR1,CR2
  Correct prediction ratios for the two binary responses as percentage.

Details

As in the package mgcv, based on the results of Marra and Wood (2012), `Bayesian p-values' are returned for the smooth terms. These have better frequentist performance than their frequentist counterpart. Let $\hat{\bf f}$ and ${\bf V}_f$ denote the vector of values of a smooth term evaluated at the original covariate values and the corresponding Bayesian covariance matrix, and let ${\bf V}_f^{r-}$ denote the rank $r$ pseudoinverse of ${\bf V}_f$. The statistic used is $T=\hat{\bf f}^\prime {\bf V}_f^{r-} \hat{\bf f}$. This is compared to a chi-squared distribution with degrees of freedom given by $r$, which is obtained by biased rounding of the estimated degrees of freedom. See Marra (2013) for further details. Note that covariate selection can also be achieved using a shrinkage approach as shown in Marra and Wood (2011).

References

Diebold F.X. and Rudebusch G.D. (1989), Scoring the Leading Indicators. Journal of Business, 62(3), 369-391. Marra G. (2013), On P-values for Semiparametric Bivariate Probit Models. Statistical Methodology, 10(1), 23-28. Marra G. and Wood S.N. (2011), Practical Variable Selection for Generalized Additive Models. Computational Statistics and Data Analysis, 55(7), 2372-2387. Marra G. and Wood S.N. (2012), Coverage Properties of Confidence Intervals for Generalized Additive Model Components. Scandinavian Journal of Statistics, 39(1), 53-74.

See Also

AT, InfCr, SemiParBIVProbitObject, plot.SemiParBIVProbit, predict.SemiParBIVProbit

Examples

## see examples for SemiParBIVProbit